Linear Algebra and Its Applications

ISBN-10: 0155510053
ISBN-13: 9780155510050
Edition: 3rd 1988
List price: $147.95
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Description: With a highly applied and computational focus, this book combines the important underlying theory with examples from electrical engineering, computer science, physics, biology and economics. An expanded list of computer codes in an appendix and more  More...

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Book details

List price: $147.95
Edition: 3rd
Copyright year: 1988
Publisher: Brooks/Cole
Publication date: 2/10/1988
Binding: Hardcover
Pages: 520
Size: 6.50" wide x 9.75" long x 1.00" tall
Weight: 1.694
Language: English

With a highly applied and computational focus, this book combines the important underlying theory with examples from electrical engineering, computer science, physics, biology and economics. An expanded list of computer codes in an appendix and more computer-solvable exercises in the text reflect Strang?s interest in computational linear algebra. Many exercises appear in the sections and in the chapter reviews. Exercises are simple but instructive.

Matrices and Gaussian Eliminationp. 1
Introductionp. 1
The Geometry of Linear Equationsp. 3
An Example of Gaussian Eliminationp. 11
Matrix Notation and Matrix Multiplicationp. 19
Triangular Factors and Row Exchangesp. 32
Inverses and Transposesp. 45
Special Matrices and Applicationsp. 58
Review Exercises: Chapter 1p. 65
Vector Spacesp. 69
Vector Spaces and Subspacesp. 69
Solving Ax = 0 and Ax = bp. 77
Linear Independence, Basis, and Dimensionp. 92
The Four Fundamental Subspacesp. 102
Graphs and Networksp. 114
Linear Transformationsp. 125
Review Exercises: Chapter 2p. 137
Orthogonalityp. 141
Orthogonal Vectors and Subspacesp. 141
Cosines and Projections onto Linesp. 152
Projections and Least Squaresp. 160
Orthogonal Bases and Gram-Schmidtp. 174
The Fast Fourier Transformp. 188
Review Exercises: Chapter 3p. 198
Determinantsp. 201
Introductionp. 201
Properties of the Determinantp. 203
Formulas for the Determinantp. 210
Applications of Determinantsp. 220
Review Exercises: Chapter 4p. 230
Eigenvalues and Eigenvectorsp. 233
Introductionp. 233
Diagonalization of a Matrixp. 245
Difference Equations and Powers A[superscript k]p. 254
Differential Equations and e[superscript At]p. 266
Complex Matricesp. 280
Similarity Transformationsp. 293
Review Exercises: Chapter 5p. 307
Positive Definite Matricesp. 311
Minima, Maxima, and Saddle Pointsp. 311
Tests for Positive Definitenessp. 318
Singular Value Decompositionp. 331
Minimum Principlesp. 339
The Finite Element Methodp. 346
Computations with Matricesp. 351
Introductionp. 351
Matrix Norm and Condition Numberp. 352
Computation of Eigenvaluesp. 359
Iterative Methods for Ax = bp. 367
Linear Programming and Game Theoryp. 377
Linear Inequalitiesp. 377
The Simplex Methodp. 382
The Dual Problemp. 392
Network Modelsp. 401
Game Theoryp. 408
Intersection, Sum, and Product of Spacesp. 415
The Jordan Formp. 422
Solutions to Selected Exercisesp. 428
Matrix Factorizationsp. 474
Table of Contents provided by Ingram. All Rights Reserved.

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